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Dana Ernst

  • PhD Mathematics
  • Assistant Professor
  • Northern Arizona University
  • 1

    h-index

    Impact measure calculated by Scopus using these publications and citation counts.
  • 5

    Citations

    Number of citations received by these publications in Scopus.

Research interests

impartial gamescombinatorial game theoryscholarship of teaching and learning (SoTL)inquiry-based learning (IBL)diagram algebrasHecke algebrasCoxeter groupsgeneralized Temperley–Lieb algebrasKazhdan–Lusztig theory

About

My name is Dana Ernst and I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of Coxeter groups and their associated Hecke algebras, Kazhdan-Lusztig theory, generalized Temperley-Lieb algebras, diagram algebras, and heaps of pieces. By employing combinatorial tools such as diagram algebras and heaps of pieces, one can gain insight into algebraic structures associated to Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. More recently, my research has expanded into combinatorial game theory (joint with Nandor Sieben and Bret Benesh). In particular, our research has focused on avoidance and achievement games involving finite groups. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible. My interests also include the scholarship of teaching and learning (SoTL) with a focus on inquiry-based learning (IBL) as an approach to teaching/exploring mathematics. I am currently a Special Projects Coordinator for the Academy of Inquiry-Based Learning and a mentor for several new IBL practitioners. Moreover, I actively give talks and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement this approach in the mathematics classroom. Lastly, I am a husband and a father of two incredible sons. Oh, I enjoy drinking copious amounts of coffee, too. For more information, see my webpage: http://dcernst.github.io.

Co-authors (12)

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Publications

Cominuscule elements of Coxeter groups of type affine $C$

  • Ernst D
  • Green R
In preparation (2016)
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Conjugacy classes of cyclically fully commutative elements in Coxeter groups of type $A$

  • Ernst D
  • Fox B
In preparation (2016)
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Impartial achievement and avoidance games for generating generalized dihedral groups

  • Benesh B
  • Ernst D
  • Sieben N
{\tt arXiv:1608.00259} (2016)
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T-avoiding elements of Coxeter groups

  • Ernst D
  • Laird T
In preparation (2016)
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The many faces of IBL

Handbook of Research on Pedagogical Practice in STEM Education (2015)
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Professional experience

Assistant Professor

Northern Arizona University

August 2012 - Present

Assistant Professor

Plymouth State University

August 2008 - May 2012(4 years)

Graduate Student

University of Colorado Boulder

September 2003 - August 2008(5 years)

Faculty

Front Range Community College

September 2001 - May 2003(2 years)

Graduate Teaching Assistant & Instructor

Northern Arizona University

August 1997 - May 2001(4 years)

Education history

PhD, Mathematics

University of Colorado Boulder

September 2003 - August 2008(5 years)

MS, Mathematics

Northern Arizona University

August 1997 - May 2000(3 years)

BS, Mathematics

George Mason University

September 1993 - May 1997(4 years)